Coupled harmonic oscillators, generalized harmonic-oscillator eigenstates and coherent states

1996 ◽  
Vol 111 (7) ◽  
pp. 811-823 ◽  
Author(s):  
G. Dattoli ◽  
A. Torre ◽  
S. Lorenzutta ◽  
G. Maino
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Generalized Harmonic Oscillator

Coherent states for Smorodinsky-Winternitz potentials

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Nuri Ünal
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Wave Packets ◽  
Harmonic Oscillators ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Cartesian Coordinates ◽  
Physical Time ◽  
First Case

AbstractIn this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.

scholarly journals Simple representation of the quantum entanglement of coupled harmonic oscillators in terms of the reflection coefficient

2021 ◽  
Vol 2086 (1) ◽  
pp. 012171
Author(s):  
Yu V Tsykareva ◽  
D N Makarov
Keyword(s):  
Reflection Coefficient ◽  
Harmonic Oscillator ◽  
Quantum Entanglement ◽  
Simple Form ◽  
Harmonic Oscillators ◽  
Quantum Metrology ◽  
Molecular Chemistry ◽  
Coupled Harmonic Oscillators ◽  
Modern Physics ◽  
Coupled Harmonic Oscillator

Abstract Quantum entanglement of coupled harmonic oscillators is frequently applied in quantum and non-linear physics, molecular chemistry and biophysics, which is why its study is of a great interest for modern physics. In this work a quantum entanglement of a coupled harmonic oscillator in a simple form was found. This simple form is presented as a single parameter – reflection coefficient R. All parameters of the studied system are included in the R coefficient. It is shown that the derivation of the expression can have applications in quantum optics, in particular in quantum metrology.

scholarly journals Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators

2019 ◽  
Vol 1 (2) ◽  
pp. 260-270 ◽  
Author(s):  
James Moran ◽  
Véronique Hussin
Keyword(s):  
Harmonic Oscillator ◽  
Configuration Space ◽  
Coherent States ◽  
Probability Density Functions ◽  
Harmonic Oscillators ◽  
Uncertainty Relations ◽  
Density Functions ◽  
Ladder Operators ◽  
New States ◽  
2D System

In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the S U ( 2 ) coherent states, where these are then used as the basis of expansion for Schrödinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.

Even and odd coherent states of supersymmetric harmonic oscillators and their nonclassical properties

2016 ◽  
Vol 30 (07) ◽  
pp. 1650026 ◽  
Author(s):  
Davood Afshar ◽  
Amin Motamedinasab ◽  
Azam Anbaraki ◽  
Mojtaba Jafarpour
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Bell States ◽  
Harmonic Oscillators ◽  
Nonclassical Properties ◽  
Logical Qubits ◽  
Poissonian Statistics

In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

scholarly journals NON-HERMITIAN OSCILLATOR-LIKE HAMILTONIANS AND λ-COHERENT STATES REVISITED

2001 ◽  
Vol 16 (02) ◽  
pp. 91-98 ◽  
Author(s):  
JULES BECKERS ◽  
NATHALIE DEBERGH ◽  
JOSÉ F. CARIÑENA ◽  
GIUSEPPE MARMO
Keyword(s):  
Harmonic Oscillator ◽  
Hilbert Spaces ◽  
Coherent States ◽  
Scalar Product ◽  
Points Of View ◽  
Usual Scalar ◽  
Usual Scalar Product

Previous λ-deformed non-Hermitian Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of self-adjointness. The corresponding deformed λ-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.

Coherent states for nonlinear harmonic oscillator and some of its properties

2015 ◽  
Vol 56 (6) ◽  
pp. 062108 ◽  
Author(s):  
Naila Amir ◽  
Shahid Iqbal
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States
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